At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere ? (Given : Mass of oxygen molecule (m) `= 2.76 xx 10^(-26) kg` , Boltzmann's constant `k_B = 1.38 xx 10^(-23) JK^(-1)` )

Options

A. `1.254xx10^(4)K`
B. `2.508 xx10^(4)K`
C. `5.016 xx10^4K`
D. `8.360 xx10^4K`

Answer

D

Explanation

`v_e = sqrt((3k_BT)/m)`
`:. v_e^2=(3k_BT)/m`
`:. T = (v_E^2)/(3k_B)`
`:. T = ((11.2xx10^3)^2 xx2.76 xx10^(-26))/(3xx1.38 xx 10^(-23))`
`:. T = 83.626 xx10^3`
`= 8.363 xx10^4 K`
`:. T ~~ 8.360 xx 10^4 K` (Approx)